Visual maps are crucial for visual function. Understanding the mechanisms by which visual maps develop and regenerate is therefore crucial for understanding how vision develops, and how vision could be restored after injury. Perhaps the most important model system for visual map development is the topographic projection from the retina to the tectum/superior colliculus. Although the mechanisms of map formation in this system have been studied experimentally for many decades, there is no unifying theoretical framework that can explain more than a small subset of this data. Without such a framework it is impossible to rigorously state what the mechanisms underlying map formation in the retinotectal system really are, and it is difficult to extrapolate beyond current data to predict how novel perturbations to the system will affect map development. Although several theoretical models of retinotectal map formation have been proposed previously, they have two serious limitations. Firstly, they generally address only refinements to map topography by activity-dependent Hebbian learning rules, and do not address how initial topography forms by activity independent processes. Secondly, they generally take no account of any of the data that has emerged since 1995 on the crucial role of ephrin/Eph gradients in retinotectal map formation. To overcome these problems, we propose to develop a comprehensive new model which (1) is based on axon guidance by molecular gradients rather than Hebbian learning rules, and (2) synthesizes recent data on ephrin/Eph gradients with older data regarding surgical manipulations to the system. The PI is in a unique position to be able to do this, since he combines a detailed knowledge of the extensive experimental data in this area with wide-ranging experience in the theoretical modeling of axon guidance and map formation in the visual system. The outcome of this project will be a computational framework that rigorously identifies the relative contributions of mechanisms such as chemotaxis and competition to the formation of retinotectal maps, makes testable predictions, and can guide future experimental work.